On semilinearity in formal power series
نویسنده
چکیده
A notion of semilinearity is introduced for formal power series as a natural generalization of semilinear languages over a commutative monoid. Some closure properties of the semilinear languages are established also for formal power series. In this way, a classical result due to Eilenberg and Sch utzenberger and some results due to Ginsburg are extended to series. We also prove that Parikh's theorem does not hold for series unless some rather constraining conditions are considered.
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